Spectral stability for subsonic traveling pulses of the Boussinesq `abc' system

Abstract

We consider the spectral stability of certain traveling wave solutions of the Boussinesq `abc' system. More precisely, we consider the explicit $sec{h}^2(x)$ like solutions of the form $(\vp(x-w t), ψ(x- w t)=(\vp, const. \vp)$, exhibited by M. Chen (1998) and we provide a complete rigorous characterization of the spectral stability in all cases for which $a=c<0,b>0$.